pub fn new_birthday_probability(n: u32) -> f64 {
    if n >= 365 {
        return 1.0;
    }
    let mut p_diff = 1.0;
    for i in 1..=n {
        p_diff *= (365 - i + 1) as f64 / 365.0;
    }
    1.0 - p_diff
}
